4t^2-11=2

Solution for 4t^2-11=2 equation:

4t^2-11=2

We move all terms to the left:

4t^2-11-(2)=0

We add all the numbers together, and all the variables

4t^2-13=0

a = 4; b = 0; c = -13;
Δ = b2-4ac
Δ = 02-4·4·(-13)
Δ = 208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{13}}{2*4}=\frac{0-4\sqrt{13}}{8}
=-\frac{4\sqrt{13}}{8}
=-\frac{\sqrt{13}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{13}}{2*4}=\frac{0+4\sqrt{13}}{8}
=\frac{4\sqrt{13}}{8}
=\frac{\sqrt{13}}{2}
$